Question

the 6th term of an ap is -10 and the 10th term of an ap is -26 determine the 15 term of an ap

Answer 1

$a + 5d = - 10 \\ a + 9d = - 26$
From here we get
$d = - 4 \\ a = 10$
Therefore, 15th term
$a + (15 - 1)d = 10 + 14( - 4) = 10 - 96 = - 86$

Answer 2

a+5d=-10
a+9d=-26
d=-4
a=10
a+14d=-46